Spacecraft attitude control using nonlinear H_∞ output-feedback

We propose a computational scheme for solving the output-feedback H_∞ control problem, for a class of nonlinear systems with polynomial vector field. By converting the resulting Hamilton-Jacobi inequalities from rational forms to their equivalent polynomial forms, we overcome the non-convex nature and numerical difficulty. Using quadratic Lyapunov functions, both the state-feedback and output-feedback problems are reformulated as semi-definite optimization conditions, while locally tractable solutions can be obtained through sum of squares (SOS) programming. We show that our computational scheme results in a better disturbance attenuation closed-loop system, than the standard optimal and proportional controllers.